Counting Numbers:

### {1, 2, 3, 4, 5, 6, ...}

BY THE WAY, "..." notates continuation going up infinitely.

The set of **Natural Numbers** \( \mathbb{N}\ \ \) = {0, 1, 2 3, 4, 5, 6...}.

The set of **Integers**, \( \mathbb{Z}\ \ \) = {..., -3, -2, -1, 0, 1, 2, 3}.

The set of **Rational numbers**, \( \mathbb{Q}\ \ \) is the set of ratios of integers.

That is, every \(q \in \mathbb{Q}\ \)

is of the form:

\( q = \frac{n}{m} \ \)

With \( n, m \in \mathbb{Z}\ \) .

The set of **Real Numbers** \( \mathbb{R}\ \ \) is the set of limits of sequences of rational numbers.

A **set **is a collection of "elements," or "members," and each set is entirely determined by its members. If \[ x \]is a member of a set \[ U, \] we write \[ x \in U. \] In basic algebra, the elements of a set are usually numbers.

We can also designate a set by enclosing its members in braces , { }.